Foundations of Physics Letters

, Volume 10, Issue 1, pp 43–60 | Cite as

The logic of quantum mechanics derived from classical general relativity



For the first time it is shown that the logic of quantum mechanics can be derived from classical physics. An orthomodular lattice of propositions characteristic of quantum logic, is constructed for manifolds in Einstein’s theory of general relativity. A particle is modelled by a topologically non-trivial 4-manifold with closed timelike curves—a 4-geon, rather than as an evolving 3-manifold. It is then possible for both the state preparationand measurement apparatus to constrain the results of experiments. It is shown that propositions about the results of measurements can satisfy a non-distributive logic rather than the Boolean logic of classical systems. Reasonable assumptions about the role of the measurement apparatus leads to an orthomodular lattice of propositions characteristic of quantum logic.

Key words

geons closed timelike curves quantum mechanics general relativity quantum logic 


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  1. 1.
    E. G. Beltrametti and G. Cassinelli,The Logic of Quantum Mechanics (Addison-Wesley, Reading, 1981).MATHGoogle Scholar
  2. 2.
    S. S. Holland, Jr.,Bull. Am. Math. Soc. 32, 205 (1995).MATHMathSciNetGoogle Scholar
  3. 3.
    A. Einstein and Rosen,Phys. Rev. 48, 73 (1935).MATHCrossRefADSGoogle Scholar
  4. 4.
    C. W. Misner and J. A. Wheeler,Ann. Phys. 2, 525 (1957).MATHCrossRefADSMathSciNetGoogle Scholar
  5. 5.
    J. Friedman, M. S. Morris, I. D. Novikov, and U. Yurtsever,Phys. Rev. D 42, 1915 (1990).CrossRefADSMathSciNetGoogle Scholar
  6. 6.
    K. S. Thorne, “Closed timelike curves” inProceedings, 13th International Conference on General Relativity and Gravity, 1992 (Institute of Physics Publishing, Bristol, 1992).Google Scholar
  7. 7.
    L. E. Ballentine,Quantum Mechanics (Prentice Hall, New Jersey, 1989).Google Scholar
  8. 8.
    P. R. Holland,The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1993).Google Scholar
  9. 9.
    P. A. Schilpp, ed.,Albert Einstein: Philosopher-Scientist (Cambridge University Press, Cambridge, 1970).Google Scholar
  10. 10.
    J. L. Friedman and R. D. Sorkin,Gen. Rel. Grav. 14, 615 (1982).ADSMathSciNetGoogle Scholar
  11. 11.
    J. M. Jauch,Foundations of Quantum Mechanics (Addison-Wesley, Reading, 1968).MATHGoogle Scholar
  12. 12.
    C. J. Isham, “Structural issues in quantum gravity,” plenary session lecture given at the GRG 14 Conference, Florence, grqc/9510063, August 1995.Google Scholar
  13. 13.
    R. Penrose,Rev. Mod. Phys. 137, 215 (1973).MathSciNetGoogle Scholar
  14. 14.
    D. N. Page and C. D. Geilker,Phys. Rev. Lett. 147, 979 (1981).CrossRefADSMathSciNetGoogle Scholar
  15. 15.
    L. E. Ballentine and J. P. Jarrett,Am. J. Phys. 155, 696 (1987).CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of WarwickCoventryUnited Kingdom

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